Question

A particle is travelling along a straight line $OX$. The distance $x$ (in metres) of the particle from $O$ at a time $t$ is given by $X=37+27t-t^{3}$ where $t$ is time in seconds. The distance of the particle from $O$ when it comes to rest is

• A. 81 m
• B. 91 m
• C. 101 m
• D. 111 m

Answer 1

Answer: (B)

91 m

Answer 2

Given, $x=37 +27 t-t^{3}$
$v=\frac{d x}{d t}=27-3 t^{2}$
According to problem,
$v=0 \Rightarrow 27-3 t^{2}=0$
Here, $t=3 s$
$x=37+27 \times 3-(3)^{2}=91\, m$